Compensating asymmetries of signals using piece-wise linear approximation

ABSTRACT

A system including a first circuit, a second circuit, an amplifier, and a summer. The first circuit is configured to (i) select a first portion of a signal, and (ii) generate a first compensation for asymmetry in the first portion of the signal using a first function, where the first function is a modulus function. The second circuit is configured to (i) select a second portion of the signal, and (ii) generate a second compensation for asymmetry in the second portion of the signal using a second function, where the second function is different than the first function. The amplifier amplifies the signal and provides an amplified output. The summer is configured to add (i) the first compensation, (ii) the second compensation, and (iii) the amplified output, where (i) the first circuit, (ii) the second circuit, and (iii) the amplifier are connected in parallel to the summer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 13/453,584,filed on Apr. 23, 2012, which is a continuation of U.S. patentapplication Ser. No. 11/835,936 (now U.S. Pat. No. 8,164,845), filed onAug. 8, 2007. The entire disclosures of the above applications areincorporated herein by reference.

BACKGROUND

Hard disk drive transducing heads, including magneto-resistive (MR)heads, can provide an asymmetric output for a variety of reasons wellknown to ordinarily skilled artisans. Such reasons include, but are notlimited to age, temperature, thermal asperity, current changes, and thelike. When an output is asymmetric, the output waveform, desirablysubstantially sinusoidal, can have a positive portion of the waveformthat is more substantial than a negative portion thereof (or viceversa).

Various asymmetry correction approaches have been tried over the years,including providing second order and/or third order corrections, orexponential corrections, or corrections which include a modulusfunction. One deficiency in these approaches is their validity extendsonly within a relatively limited range of unsaturated states of thehead. Outside of that limited range, the results tend to diverge, andare less desirable.

FIGS. 1 a-1 c are sample saturation curves that are plots of resistanceas a function of magnetic flux. There is a portion of these curves, inthe vicinity of a value I_(bias), that is substantially linear. Headingin either direction on these curves away from the value I_(bias), thecurves have nonlinear characteristics that can be modeled in differentways. The areas on these curves outside of the outermost circlescorrespond to saturated states. In FIG. 1 a, the area around I_(bias) ismodeled using a purely linear function such as y=αx. As can be seen inFIG. 1 a, the linear approximation works in a portion, but not in all ofthe unsaturated region.

FIG. 1 b shows the same curve, this time with a model based on anexponential or second/third order function such as y=αx^(n). Again,while the model holds through part of the unsaturated region, it doesnot hold throughout. Finally, FIG. 1 c shows the same curve again, thistime with a model based on a modulus function such as y=α|x|+x, where adark dot shows a change (break point) in the slope of the line based onthe modulus function. As can be seen, once again, while this model holdsthrough part of the unsaturated region, it does not hold throughout.

In view of this and other deficiencies, it would be desirable to have anasymmetry correction system which provides a valuable approximation toan appropriate asymmetry correction over a wider range.

BRIEF DESCRIPTION OF DRAWINGS

The invention now will be described in detail with reference to one ormore embodiments and also with reference to the following drawings, inwhich:

FIGS. 1 a-1 c depict various aspects of graphs of asymmetry correction;

FIG. 2 is a high-level block diagram of a portion of a read channelaccording to one embodiment of the present invention;

FIGS. 3 a and 3 b are a block diagram of one portion of an asymmetrycorrection circuit according to one embodiment of the invention, and agraph depicting the output of that circuit respectively;

FIG. 4 is a block diagram of another embodiment of one portion of anasymmetry correction circuit according to the present invention;

FIGS. 5 a-5 c are graphs describing an output of the circuit of FIG. 4;

FIG. 6 is a block diagram of another embodiment of the invention;

FIG. 7 is a graph of one possible output of the circuit of FIG. 6; and

FIG. 8 is a more detailed circuit diagram of one portion of an asymmetrycorrection circuit according to one embodiment of the present inventionas used for example, in FIG. 4.

DESCRIPTION

To achieve the foregoing and other objects, in accordance with oneembodiment of the invention, a piece-wise linear approximation to anasymmetry correction curve is provided, in which the number of pieces isselectable, and the type of correction (e.g. linear, exponential,higher-order, modulus) provided for each of the pieces also isselectable.

Objects and advantages of the present invention will become apparentfrom the following detailed description. For convenience, the followingdescription refers to MR heads, but the invention is applicable to anyapparatus in which asymmetry correction is necessary.

Referring to FIG. 2, the signals from an MR head pass to variable gainamplifier (VGA) 20, and then to an asymmetry correction block 200. Theoutput of that correction block 200 is filtered and provided to aprocessing block 210. The processing block 210 includes a filter 212, ananalog-to-digital converter (ADC) 214, and a further filter such as afinite impulse response (FIR) filter 216. Skilled artisans willappreciate that the processing block 210 can have numerous variants,including but not limited to the number and types of filters containedtherein.

FIG. 3 a is a diagram of one embodiment of circuitry for implementingthe function y=α|x|+x. As can be seen in FIG. 3 a, the value for x isprovided to an amplifier 302 which in one embodiment has a gain of 1,but which in other embodiments can have various gain values as desired.The output i₁ from that amplifier 302 is provided to a summer 310. Thevalue for x also goes into an amplifier 306 that provides a modulus orabsolute value of x. The output of that amplifier 306 is multiplied in ablock 308 by a scaling factor of α which is selectable according to thecorrection to be provided. The output i₂ from that α block 308 also ispassed to the summer 310, and the output of the summer 310 is thedesired function y.

FIG. 3 b shows the graph of y=βx+α|x|. Also shown is a dotted line y=βx,where β is the value of the gain of the amplifier in FIG. 3 a. α|x| isshown as well. The solid line with large dots shows the actual value ofy=βx+α|x|, where α|x| is always greater than or equal to 0.

FIG. 4 shows a block similar to FIG. 3 a, except that a value which isan offset of d is added going into the amplifier 306 that provides themodulus of x. The dotted line around the offset block 406 and theamplifier 408 identify circuitry, the output of which is function of xand d. d may be 0, or a positive value, or a negative value, dependingon the portion of the curve in FIG. 3 a for which compensation, orpiece-wise linear approximation is being provided. d simply shifts thecompensation graph to the left or right, depending on the position ofinterest on the saturation curve relative to the origin.

In FIG. 4, the input x goes into an amplifier 402 where it is amplifiedby a factor of β, where β can be 1 in one embodiment, or different from1 in other embodiments. The output of that amplifier 402, i₁ goes to asummer 412, similarly to the case in FIG. 3 a.

The value x also goes into a correction block 404 which includes anoffset block 406, as noted previously, and a modulus amplifier 408. Theoutput of that modulus amplifier 408, y₁, is scaled by a scaler 410 witha factor α, and the output i₂, also passes through the summer 412 toyield the result y.

FIG. 5 a and FIG. 5 b show respectively graphs of current as a functionof the input voltage, and also show a graph of a resulting modulusfunction based on an offset d which, to accomplish the graph in FIG. 5b, is negative. As shown in FIG. 5 c, to the left of the offset value d,the slope of the line changes. If the offset d had been positive ratherthan negative, the slope in the upper right quadrant would have changed,per the dotted line, rather than changing in the lower left quadrant, asshown in FIG. 5 c. If d had been zero, the graph would have beensymmetric around the Y axis.

FIG. 6 shows an embodiment of the invention which accomplishes multiplebreaks, to provide multiple piece-wise linear approximations. Since asecond order compensation, or a third order compensation, or both, orcompensations of other orders, or modulus compensation may be necessaryat different parts of the curve, the provision of multiple break pointsenables local tuning of the compensation curve in order to provideaccurate compensation. In FIG. 6, the input x goes into an amplifier 602where it is amplified by a gain of β which in one embodiment is 1) andthe output is passed to a summer 612. The input x also passes into ablock 604 ₁ where an offset d₁ is provided in block 606 ₁, the output ofthat block 606 ₁ going to a modulus amplifier 608 ₁. The output i₁ ofthat amplifier 608 ₁ is scaled by a scalar 610 ₁ with a factor α₁ andthe output, i₁, passes to the summer 612. Also shown, in the same manneras for the offset d₁, there is a block line for providing an offset d₂,and below that, the provision of an offset d₃. Each of the amplifiers608 _(I) may be modulus amplifiers, or exponential-order amplifiers, orany desired combination of these, depending on the amount or type ofcontrol that the user wants or needs over the asymmetry correctionprocess.

As many breakpoints, or as few breakpoints as desired (a number N areshown in FIG. 6) may be provided. The summer 612 thus sums all of thecurrents i₀ through i_(n), and the resulting output y may be representedby the following equation:

$y = {x + {\sum\limits_{i = 1}^{n}\;{\alpha_{i}{f_{i}\left( {x,d_{i}} \right)}}}}$

For each of the individual blocks providing offsets d₁, d₂, . . . ,d_(n), y=f(x,d). The following relationships pertain:

${\left. {{{\left. {\begin{matrix}{{y_{1} = x},\;{x > d}} \\{{y_{1} = {- \left( {x + {2d}} \right)}},}\end{matrix}\begin{matrix}\; \\{x \leq d}\end{matrix}} \right\} d} < 0}\begin{matrix}{{y_{1} = {x - {2d}}},} & {x \geq d} \\{{y_{1} = {- x}},} & {x < d}\end{matrix}} \right\} d} \geq 0$

One advantage of the arrangement of FIG. 6 is that the combination ofthe various blocks is linear. Thus, for example, where an overallscaling of a might be desirable, α can be split into smaller blocks. Thecorresponding transistors for those blocks can be smaller. As a result,in one embodiment, the same amount of real estate on a wafer can be usedfor the overall α as for the combination of the various smaller α. Thedifference is that the channel designer is provided with more variables,thus providing more control and more precise curve fitting.

One result of the embodiment of FIG. 6 is shown in the graph of FIG. 7,which is a curve with a number of segments.

As can be appreciated from the foregoing, the amount of complexity ofthe overall circuit is a linear function of the number of breakpointsdesired. For example, providing four breakpoints would result in roughlyfour times the complexity of an implementation with a single breakpoint.

FIG. 8 shows a transistor level version of one embodiment of one of thecells for a particular breakpoint of FIG. 6, using modulus functionimplementation, as shown for example in FIG. 4. In FIG. 8, the inputvoltage x is provided to an amplifier 802, which provides a gain of β,as described before. x also is provided to the two inputs of a switchingamplifier 804 which switches direction according to a desired zerocrossing (d). One output of the switching amplifier 804 is provided totransistors 812, 818, and the other output is provided to transistors814, 816. When transistors 812, 818 are on, transistors 814, 816 areoff, thus directing the current in a desired direction. With transistors812, 818 on and transistors 814, 816 off, in a first half cycle, currentflows in an upward direction in FIG. 8, and in a subsequent half cycle,with transistors 812, 818 off and transistors 814, 816 on, current flowsin a downward direction. In this manner, a modulus x function isprovided. Transistors 822, 824, respectively, provide a linear gain ofα, where α is programmed by the current through transistor 830, andthrough variable resistors 826, 828.

The value of α will define the amount of compression or expansion of awaveform in order to provide a substantially sinusoidal waveform,compensating for asymmetry. Changing d and α changes the slopes andbreakpoints, and provides a piece-wise linear approximation of a fairlyprecise magneto-resistive asymmetry.

As can be appreciated from the foregoing, according to the invention,using circuitry that is easily implementable and provides piece-wiselinear functions, any desired asymmetry compensation of any order can beapproximated within a desired range.

While the foregoing description has been provided with respect to one ormore embodiments, various modifications within the scope and spirit ofthe invention will be apparent to those of working skill in the relevanttechnological field. Thus, the invention is to be limited by the scopeof the following claims.

A non-transitory computer program product containing program code forperforming a method for compensating for asymmetry in waveform of aninput signal is also provided. The method includes outputting a firstcompensation as a first function and outputting a second compensation asa second function. The first and second compensations together provide apiecewise approximation to at least one region of a saturation curve.

What is claimed is:
 1. A system comprising: a first circuit configuredto (i) select a first portion of a signal, and (ii) generate a firstcompensation for asymmetry in the first portion of the signal using afirst function, wherein the first function is a modulus function; asecond circuit configured to (i) select a second portion of the signal,and (ii) generate a second compensation for asymmetry in the secondportion of the signal using a second function, wherein the secondfunction is different than the first function; an amplifier configuredto amplify the signal and to provide an amplified output; and a summerconfigured to add (i) the first compensation, (ii) the secondcompensation, and (iii) the amplified output, wherein (i) the firstcircuit, (ii) the second circuit, and (iii) the amplifier are connectedin parallel to the summer.
 2. The system of claim 1, wherein: the firstfunction is of a form γ=βx+α|x|; and the second function is (i) a linearfunction of a form γ=αx, (ii) an exponential function of a formγ=αe^(x), or (iii) a polynomial function of a form$\sum\limits_{i = 0}^{n}\;{\alpha\;{{ix}^{i}.}}$
 3. The system of claim1, wherein: the first circuit is configured to (i) select the firstportion of the signal based on a first offset, (ii) amplify the firstportion of the signal according to the first function, and (iii) scalethe amplified first portion based on a first factor to generate thefirst compensation; and the second circuit configured to (i) select thesecond portion of the signal based on a second offset, (ii) amplify thesecond portion according to the second function, and (iii) scale theamplified second portion based on a second factor to generate the secondcompensation.
 4. The system of claim 3, wherein the first offset, thesecond offset, the first factor, and the second factor determine slopesand breakpoints of the first portion and the second portion of thesignal.
 5. The system of claim 3, wherein each of the first factor andthe second factor determines an amount of compression or expansion ofthe signal to compensate for the asymmetry.
 6. The system of claim 1,wherein the first compensation and the second compensation provide apiecewise approximation of a region of the signal, and wherein theregion includes at least the first portion and the second portion of thesignal.
 7. The system of claim 1, wherein the first compensation and thesecond compensation are used to compensate an asymmetry in a waveform ofthe signal using a piecewise approximation.
 8. A method comprising:selecting (i) a first portion of a signal, and (ii) a second portion ofthe signal; generating a first compensation for asymmetry in the firstportion of the signal using a first function, wherein the first functionis a modulus function; generating a second compensation for asymmetry inthe second portion of the signal using a second function, wherein thesecond function is different than the first function; amplifying thesignal; receiving, in parallel, (i) the first compensation, (ii) thesecond compensation, and (iii) the amplified signal; and adding, inparallel, (i) the first compensation, (ii) the second compensation, and(iii) the amplified signal.
 9. The method of claim 8, wherein: the firstfunction is of a form γ=βx+α|x|; and the second function is (i) a linearfunction of a form γ=αx, (ii) an exponential function of a formγ=αe^(x), or (iii) a polynomial function of a form$\sum\limits_{i = 0}^{n}\;{\alpha\;{{ix}^{i}.}}$
 10. The method of claim8, further comprising: selecting (i) the first portion of the signalbased on a first offset, and (ii) the second portion of the signal basedon a second offset; amplifying (i) the first portion of the signalaccording to the first function, and (ii) the second portion accordingto the second function; and scaling (i) the amplified first portionbased on a first factor to generate the first compensation, and (ii) theamplified second portion based on a second factor to generate the secondcompensation.
 11. The method of claim 10, wherein the first offset, thesecond offset, the first factor, and the second factor determine slopesand breakpoints of the first portion and the second portion of thesignal.
 12. The method of claim 10, wherein each of the first factor andthe second factor determine an amount of compression or expansion of thesignal to compensate for the asymmetry.
 13. The method of claim 8,further comprising: generating a piecewise approximation of a region ofthe signal based on (i) the first compensation and (ii) the secondcompensation, wherein the region includes at least the first portion andthe second portion of the signal.
 14. The method of claim 8, furthercomprising compensating an asymmetry in a waveform of the signal using apiecewise approximation generated based on (i) the first compensationand (ii) the second compensation.